There is a serious conversation worth having about term limits and the Los Angeles County Board of Supervisors. Supporters of the limits — currently three terms of four years each — argue that they are necessary because once supervisors are in office, they're impervious to challenge. Their districts are too big, scrutiny too light, their ability to raise money too great. Critics say term limits deprive voters of choice, imbue the bureaucracy with too much power and ensure that the government is run by inexperienced leaders.

Some people support term limits for executives (mayors or governors, say) but not for legislators. But that raises the question of what kind of officials the supervisors are. Are they chief executives? They effectively serve as mayors over their 2-million-person districts. Or are they better thought of as legislators because they meet weekly to cast votes on matters that come before them as a board?

These are all questions that could fuel a thoughtful civic debate. But that's not going to happen, as our current batch of supervisors made abundantly clear last week. When the issue came up, they elected to forgo serious discussion in favor of backbiting and deflection. It was, in other words, just another week in the life of the supervisors.

The brouhaha started with Supervisor Michael D. Antonovich, the board's senior member, who slipped a sly motion onto the board's agenda late on July 20, a Friday. Antonovich proposed allowing county voters to consider a ballot measure in November that would "limit" the supervisors to five terms each. The motion didn't acknowledge that it actually would add eight years to the length of time a supervisor could serve.

Antonovich's timing suggests that he was hoping the idea would get a quick, quiet vote the following Tuesday. But by the time the board met, the measure was running into rough waters, in part because of a Times editorial that morning that sharply criticized the proposal. Supervisor Zev Yaroslavsky, for one, balked. He suggested an amendment that would have preserved the five-term idea and allowed it to extend the political lives of himself and his colleagues, but it would at least have alerted voters that they were being asked to approve an extension of existing limits, not the imposition of limits for the first time. It wasn't exactly the high road, but it was at least a middle road.

Action was postponed for a week, but when the board next took up the issue, Antonovich reluctantly agreed to support the Yaroslavsky amendment and asked in return that Yaroslavsky support his motion. Yaroslavsky didn't answer directly; still, the board approved the amendment.

But Yaroslavsky wasn't done. Having secured one amendment, he then tried for another, one that would have made most of the current board members — including himself and Antonovich — ineligible for the term extensions. Would Antonovich accept such an amendment, Yaroslavsky asked?

Putting down the snacks that he relentlessly munches during board meetings, Antonovich sputtered "Of course not!" He then accused Yaroslavsky of "following the newspaper" and said he'd rather "work with my colleagues" than kowtow to the misguided advice of the Los Angeles Times.

Yaroslavsky shrugged off that charge and responded to the underlying question: "If the issue is a philosophical one about term limits … then let's not include ourselves." And, having just been lashed by Antonovich, Yaroslavsky delivered one back. "Eleven terms is more than enough," he said. Only one supervisor would have had the potential to serve 11 terms under the measure: Antonovich.

Yaroslavsky's amendment died for lack of a second. Then it was time to vote on Antonovich's original motion, now amended to make clear that it was an extension. Antonovich and Don Knabe voted in favor; Yaroslavsky voted against, and Gloria Molina andMark Ridley-Thomas abstained, a meaningless gesture that functionally is the equivalent of voting no. Ridley-Thomas explained that he abstained because he doesn't much care about term limits (because he was first elected to the board in 2008, he's the only member not to face their constrictions any time soon); Molina declined to comment on her reasons.

Two weeks of acrimony, no serious debate, not one inch of progress. Someday L.A. County might have a thoughtful debate over term limits. Or it might not. Here's what I can promise you for sure: These supervisors won't lead it.